Evolution__3rd_Edition

..
We construct a model of selection
and migration
Polymorphism or genetic unity can
result
AA Aa aa
1 − s 1 − s 1
CHAPTER 5 / The Theory of Natural Selection 133
The A allele has frequency p in the local population. Suppose that in other subpopulations,
natural selection is more favorable to the gene A, and it has a higher frequency in
them, p m on average. p m will then be the frequency of A among immigrants to our local
population. In the local population, A genes are lost at a rate ps per generation. They are
gained at a rate (p m − p)m per generation: m is the proportion of genes that are immigrants
in a generation. Immigration increases the frequency in the local population by
an amount p m − p because gene frequency is increased only in so far as the immigrating
population has a higher frequency of A than the local population. If the immigrating
gene frequency is the same as the local gene frequency, immigration has no effect.
There are three possible outcomes. If migration is powerful relative to selection,
the rate of gain of A genes by immigration will exceed the rate of loss by selection. The
local population will be swamped by immigrants. The frequency of the A gene will
increase until it reaches p m . If migration is weak relative to selection, the frequency of
A will decrease until it is locally eliminated. The third possibility is an exact balance
between migration and selection. There will be an equilibrium (with local frequency
of A = p*) if:
Rate of gain of A by migration = rate of loss of A by selection
(p m − p*)m = p*s (5.14)
⎛ m ⎞
p* = pm⎜
⎟
(5.15)
⎝ s + m⎠
In the first case, migration unifies the gene frequencies in both populations, much in
the same manner as Section 5.14.2: migration is so strong relative to selection that it is
as if selection were not operating. In the second and third cases, migration is not strong
enough to unify the gene frequencies and we should observe regional differences in the
gene frequency; it would be higher in some places than in others. In the third case there
is a polymorphism within the local population; A is maintained by migration even
though it is locally disadvantageous.
This section has made two main points. First, a balance of migration and selection is
another process to add to the list of processes that can maintain polymorphism.
Second, we have seen how migration can be strong enough to unify gene frequencies
between subpopulations, or if migration is weaker the gene frequencies of different
subpopulations can diverge under selection. This theory is also relevant in the question
of the relative importance of gene flow and selection in maintaining biological species
(Section 13.7.2, p. 369).